Problem: As you very well know, this year's funkiest numbers are so called triangular numbers (that is, integers that are representable as <image>, where k is some positive integer), and the coolest numbers are those that are representable as a sum of two triangular numbers.

A well-known hipster Andrew adores everything funky and cool but unfortunately, he isn't good at maths. Given number n, help him define whether this number can be represented by a sum of two triangular numbers (not necessarily different)!

Input

The first input line contains an integer n (1 ≤ n ≤ 109).

Output

Print "YES" (without the quotes), if n can be represented as a sum of two triangular numbers, otherwise print "NO" (without the quotes).

Examples

Input

256


Output

YES


Input

512


Output

NO

Note

In the first sample number <image>.

In the second sample number 512 can not be represented as a sum of two triangular numbers.

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
const double eps = 1e-8;
int main() {
  long long n;
  cin >> n;
  long long s = 1, in = 1;
  vector<long long> v;
  while (s <= n) {
    v.push_back(s);
    in++;
    s += in;
  }
  long long f = 0;
  for (long long i = 0; i < (long long)v.size() && v[i] < n; i++) {
    long long req = n - v[i];
    if (binary_search(v.begin(), v.end(), req)) {
      f = 1;
      break;
    }
  }
  if (f)
    cout << "YES"
         << "\n";
  else
    cout << "NO"
         << "\n";
}